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Designing the Robot Behavior for Safe Human–Robot Interactions


Recent advances in robotics suggest that human–robot interaction (HRI) is no longer a fantasy, but is happening in various fields such as industrial robots, autonomous vehicles, and medical robots. Human safety is one of the biggest concerns in HRI. As humans will respond to the robot’s movement, interactions need to be considered explicitly by the robot. A systematic approach to design the robot behavior toward safe HRI is discussed in this chapter. By modeling the interactions in a multiagent framework, the safety issues are understood as conflicts in the multiagent system. By mimicking human’s social behavior, the robot’s behavior is constrained by the ‘no-collision’ social norm and the uncertainties it perceives for human motions. An efficient action is then found within the constraints. Both analysis and human-involved simulation verify the effectiveness of the method.


  • Human–Robot Interactions (HRI)
  • Robot Safety
  • Motion Planning
  • Human-in-the-Loop Control
  • Multiagent System

This chapter was developed and enhanced from an earlier paper published as [20] © 2015 IEEE.

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  1. 1.

    In certain cases, the open loop system may not be decoupled. For example, in the case of rehabilitation, the robot can affect the human’s dynamics directly by assisting the human to accomplish special tasks, such as walking. When the robot’s input enters the human’s dynamic equation, (11.2) does not hold.

  2. 2.

    The Lemma is proved in [18]. \(\phi \) can be constructed in the following procedure: first, check the order from \(\phi _0\) to \(u_R\) in the Lie derivative sense, denote it by n; then define \(\phi \) as \(\phi _0+k_1\dot{\phi }_0+\cdots +k_{n-1}\phi _{0}^{(n-1)}\). The coefficients \(k_1,\ldots ,k_n\) are chosen such that the roots of \(1+k_1s+\cdots +k_{n-1}s^{n-1}=0\) all lie on the negative real line.

  3. 3.

    Methods for inferring \(G_H(k)\) are discussed in [19]. In this chapter, it is assumed to be known.

  4. 4.

    The objective function is linear while the constraint function defines an ellipsoid as shown in Fig. 11.11. The optimal solution must lie on the boundary of the ellipsoid. Let \(\gamma \) be a Lagrange multiplier. Define the new cost function as:

    $$\begin{aligned} J_{j}^{*}=\frac{\partial \phi }{\partial x_{j}}x_{j}(k+1)+\gamma \left[ 9-\varDelta x_j^{T}X_{j}\left( k+1|k\right) ^{-1}\varDelta x_j\right] \end{aligned}$$

    The optimal solution satisfies \(\frac{\partial J_{j}^{*}}{\partial x_{j}(k+1)}=\frac{\partial J_{j}^{*}}{\partial \gamma }=0\), i.e., \((\frac{\partial \phi }{\partial x_{j}})^T-2\gamma X_{j}\left( k+1|k\right) ^{-1}\varDelta x_j = 0\) and \(9-\varDelta x_j^{T}X_{j}\left( k+1|k\right) ^{-1}\varDelta x_j = 0\). Then (11.40) follows.


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This work was supported in part by a Berkeley Fellowship awarded to Changliu Liu.

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Liu, C., Tomizuka, M. (2017). Designing the Robot Behavior for Safe Human–Robot Interactions. In: Wang, Y., Zhang, F. (eds) Trends in Control and Decision-Making for Human–Robot Collaboration Systems. Springer, Cham.

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